Personally, I see this like how the German Army saw the early stages of WW2, and how they planned for it. The German's plan was a series of quick, knock-out blows designed to get the major Allied powers out of the war as quickly as possible, as Germany hadn't the resources for a long war, whereas the Allies with their far reaching imperial holdings, did.

What do I mean by this?, I mean the BoS has both a technological advantage and the initial shock and awe advantage. They would be able to surge through NCR territory, capturing towns, military installations and destroying the few unprepared units they'd come across with relative ease and low casualties. However, while this sounds like a BoS god-stomp, they would *have* to keep this up, or else they'd eventually lose the war. The NCR would be like the Allies in WW2, unprepared and easy pickings at the outset of hostilities, while the BoS would be the Axis, technologically superior and using better shock doctrine. Once the NCR gets it's act together, the war will bog down at best or slowly start reversing in the NCR's favour at worst for the BoS, much like WW2, with the weight of NCR bullets, bodies and pulse grenades forcing the Brotherhood back. I'd also like to point out that the NCR doesn't discriminate, at least when it comes to military service, between mutants and sexes, too.

Tl;dr - The NCR takes massive losses at the outset in territory and men, but should it hold on enough to pull together it's strength, the Brotherhood will be forced to fight a losing retreat back to their own territory. The war will be costly, and the NCR, depending on it's losses, might even collapse internally after the BoS is driven out. But since the NCR in my eyes wins the fighting bit and post-war strife isn't the scope of the question, I'd give them the victory.

Midwestern BoS, based on what little has been established in the lore, is in pretty poor shape. The East Coast chapter barely found any evidence of their survival, meaning they are likely quite small or weak, and the Legion has reportedly captured Brotherhood scribes out east, which mean they have fought, and on several occasions, defeated the Brotherhood of Steel in the east, likely the Midwest chapter since they're the only ones in the area. The most likely canon ending of tactics would be the calculator destroyed and the BoS stranded in the wastes. Most of they're tech will be pretty broken down at this point due to a mix of wear and tear and lack of resources, not to mention many of their members are tribals who likely lack the classic Brotherhood training. Irregardless of their recruiting, this force is still dwarfed by the NCR.

Brotherhood still has tech on their side to a degree, but not to the same degree as the west coast chapters, who had the comfort of bunkers and massive supply stockpiles. Midwest BoS, going off the calculator is destroyed ending, lack those resources, and have suffered heavy losses form raiders, and later Caesar's Legion.

In my mind, NCR stomps quite easily. They just need to overwhelm them with numbers, which they have. Midwest chapter isn't strong enough to face the NCR army proper, their best bet would be guerrilla tactics, but even then, the NCR rangers would even the odds in non-conventional combat. NCR takes this.

I think it's interesting to note that the Courier when convincing Lanius not to invade Vegas, points out why no force can take the west. The west is dependant on the NCR's supply lines. All trade caravans are integrally tied to the state through congress, and all towns rely on them. NCR lacks self sufficient towns and cities, so any army advancing into NCR territory would not be able to sustain themselves in the long run because the NCR is so vast and there is no single point where they could go to in order to resupply their whole army. The NCR survives soley because all of the towns within are dependant upon the infrastructure of the NCR. A foreign force would be cut off from that infrastructure, and would quickly run low on resources. Food, water, munitions, all come from three very different parts of the NCR. Water from the caravans in the Hub, munitions from the Gun Runners in the Boneyard, food from the north in Shady... That's a vast expanse of territory to travel in order to properly plunder each place, and at each location they'd need to expand their resources in a long, drawn out battle. Taking the NCR, for a post war nation like the Brotherhood, that lacks any infrastructure (no Brotherhood chapter grows it's own food for example), that deep in foreign territory, means certain defeat. It's something to consider.

_________________Muwahahahahahahaha!!!What do you mean evil laugh!? This is how I always laugh!

What I like about FNV is that the Courier/Main Protagonist isn't necessarily immortal. Merely super skilled and lucky which means this person can be killed. In Fallout: Tactics, there was also a hero called the Warrior who in the end of the game became the Calculator and gained control of Vault 0.

So I think if there would be a battle of heroes, it would be fairly even as its a battle between a super skilled Courier vs a Vault with access to a lot of robots.

The War would be instigated by the NCR because the BOS x NCR War has not ended yet and its soldiers assumed that the BOS(Midwest) is an enemy and attacked them.

Both factions would have a reason to fight because the NCR still has some bad blood with the BOS and the BOS was attacked and retaliated in self-defense.

It would not be a stretch to say that because the BOS(Midwest) was able to reprogram a Vault 0 robot.

Vault 0 tech is also fairly reliable as they were able to almost defeat the BOS(Midwest) during the events of Fallout: Tactics.

Also all robots under Vault 0s control were deactivated when the Calculator was defeated so the question is can someone from the NCR be capable of hacking into the network of an AI augmented by human brains?

I like this analysis however I view the BOS(Midwest) as post war Soviet Russia having both technology captured from the Germans and the ability quickly mass produce stuff.

The reason why I do not see the BOS(Midwest) as Germany is because while they had access to top of the line equipment, they were not able to mass produce it as fast because everything was over engineered which is a great contrast to what the Calculator what able to do as it was almost able to wipe out all humans(in the midwest at least) by pumping out a lot of robots quickly.

In a way it would be a US x Soviet battle if they were engaged in an actual war with no sea dividing them.

This is the reason why I chose to use the Good Ending of Fallout Tactics as the other endings would make the BOS(Midwest) either too weak as a faction or lose their very diverse army(Barnaky Ending) because they wiped out all mutants. It would be a one sided match.

At least with the good ending the BOS(Midwest) would stand a chance as this was the BOS attempt to create a Utopia where all people regardless of race is united under their strict rule.

Also in this ending, they would have the technology and the number to battle a big faction such as the NCR.